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Abstract:
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In many settings, especially those in which Bayesian methodology is used, Markov chain Monte Carlo (MCMC) methods are used to draw approximate samples from otherwise intractable posterior distributions. The random-walk Metropolis (RWM) sampler is one MCMC algorithm that comes up in many situations due to its convergence guarantees and its ease of implementation. However, its convergence rate is typically assessed using ad hoc convergence assessment procedures. These techniques, while useful in determining whether or not the RWM chain has come "close enough" to the posterior distribution, do little in the way of approaching the question of how much burn-in time is required, even for subsequent runs of the same Markov chain. This work provides a computational remedy to this problem through estimation of drift and minorization coefficients through auxiliary simulations. This approach provides estimates of the mixing time of a given Markov chain without reliance on output-based convergence assessment, and this yields the ability to determine a sufficient amount of burn-in prior to running the chain. This extends the work of Spade (2015) to full Metropolis updating schemes.
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